Electromigration-induced damage in bamboo Al interconnects

Depletion and hillock formation were examined in-situ in a scanning electron microscope (SEM) during electromigration of bamboo Al interconnect segments. Hillocks formed directly at the anode ends of the segments by epitaxial addition of Al at the bottom Al/TiN interface. Depletion occurred nonuniformly from the cathode end and stopped once the distance between the leading void and the hillock reached the critical length for electromigration at the given current density. A modified equation for the drift velocity is proposed, which includes the effect of nonuniform depletion and predicts that interconnects with nonuniform depletion are more reliable than those with uniform depletion.     

Electromigration-induced failures in interconnects with bimodal grain size distributions

Interconnects containing bimodal grain size distributions are known to have lower me-dian times to electromigration-induced failure (MTTF). However, the deviation in the time to failure (DTTF) in such lines has not been well characterized. We find that Al-2%Cu-0.3%Cr interconnects with bimodally distributed grain sizes have MTTF’s which are more than an order of magnitude lower than lines with monomodally distributed small grain sizes. However, the DTTF’s for both types of lines are similar, and in fact slightly lower for lines with bimodal structures. An activation energy of 0.85 eV was obtained both for lines with monomodal large grain structures and bimodal grain struc-tures, suggesting that grain boundary diffusion is the controlling mechanism in both cases. A model based simply on microstructural characteristics,e.g. the distribution of the number of grain boundaries, can explain the lower MTTF’s and DTTF’s for lines with bimodal structures. The implications of bimodal grain size distributions on the reliability of large numbers of lines are discussed. Also, a new, convenient graphical tool for illustrating the failure rate of interconnects with lognormally distributed failure times is presented.     

Blind beamforming on a randomly distributed sensor array system

We consider a digital signal processing sensor array system, based on randomly distributed sensor nodes, for surveillance and source localization applications. In most array processing the sensor array geometry is fixed and known and the steering array vector/manifold information is used in beamformation. In this system, array calibration may be impractical due to unknown placement and orientation of the sensors with unknown frequency/spatial responses. This paper proposes a blind beamforming technique, using only the measured sensor data, to form either a sample data or a sample correlation matrix. The maximum power collection criterion is used to obtain array weights from the dominant eigenvector associated with the largest eigenvalue of a matrix eigenvalue problem. Theoretical justification of this approach uses a generalization of Szego's (1958) theory of the asymptotic distribution of eigenvalues of the Toeplitz form. An efficient blind beamforming time delay estimate of the dominant source is proposed. Source localization based on a least squares (LS) method for time delay estimation is also given. Results based on analysis, simulation, and measured acoustical sensor data show the effectiveness of this beamforming technique for signal enhancement and space-time filtering     

Stochastic geometry of network of randomly distributed moving vehicles on a highway

Vehicular ad hoc networks (VANETs) have become an extensively studied topic in contemporary research. One of the fundamental problems that has arisen in such research is understanding the network statistical properties, such as the cluster number distribution and the cluster size distribution. In this paper, we analyze these characteristics in the case in which vehicles are located on a straight road. Assuming the Rayleigh fading model and a probabilistic model of intervehicle distance, we derive probabilistic distributions of the aforementioned connectivity characteristics, as well as distributions of the biggest cluster and the number of disconnected vehicles. All of the results are confirmed by simulations carried out for the realistic values of parameters.     

取向硅钢高温退火样品晶粒尺寸、取向及磁性能关系的研究

采用EBSD技术测晶粒取向,结合晶粒形貌观察,研究了普通取向硅钢高温退火样品晶粒尺寸、取向分布和电磁性能的关系。结果表明,异常长大的晶粒主要为Goss取向,小晶粒取向较杂乱,晶粒尺寸与晶粒取向有一定的相关性;晶粒尺寸和晶粒取向分别对铁损和磁感影响较大。     

The elimination method applied to analyze wave propagation in multilayer media with randomly distributed layer parameters

A simple technique called the elimination method is proposed for calculation of the reflected and transmitted wave amplitudes in the case when two counterpropagating waves are incident on a multilayer structure with a step irregularity. The functioning of the method is exemplified by a structure consisting of ten media where the wave numbers are randomly distributed. The properties of the distribution of the reflected wave amplitude density that are due to the relationship between the structure’s thickness and the minimum wavelength in it are revealed. It is shown that a disorder in the distribution of wave numbers in the interior of the structure reduces reflection, and a parameter quantitatively characterizing this reduction is proposed.     

Simulation of the electrical properties of polycrystalline ceramic semiconductors with submicrometer grain sizes

A numerical model for the calculation of the electrical characteristics of polycrystalline ceramic semiconductors is suggested. The model is applicable in a situation where the average grain size is comparable with the depletion region width near a grain boundary and the double Schottky barriers of neighboring boundaries overlap. The two-dimensional calculation is carried out in the diffusion-drift approximation using the Voronoi grid method. The effect of crystalline grain size on the current-voltage characteristic and specific capacitance of the material is analyzed usingp-SrTiO₃ as an example.     

A grain structure based statistical simulation of electromigration damage in chip level interconnect lines

Reliability assessment of chip level interconnects is based on accelerated testing at a higher temperature and a larger current density than expected in service conditions. The critical parameters needed to extrapolate accelerated test data to service conditions are the activation energy, Q, and the current density exponent, n. Although current density exponents and activation energies are well known for the elemental processes (like void nucleation due to electromigration (EM) generated stress), there is no consensus on which apparent activation energy or current density exponent values would be applicable in reliability estimates for realistic line structures. Here, we first review our EM simulation tool. We then apply the EM simulation tool to statistical life time analysis of realistic-like line structures generated by a Monte-Carlo algorithm. For a given grain structure distribution, the stress evolution along the line is simulated, letting voids nucleate at the sites where the stress exceeds a critical level, and the nucleated voids are then allowed to grow till the largest one reaches the preset critical size, resulting in a ‘failure’ of the particular line. By repeating this process for various current densities and temperatures, it becomes possible to extract the apparent activation energies and current density exponents from the simulation data.     

Numerical simulation of stress evolution during electromigration in IC interconnect lines

A finite element simulation of stress evolution in thin metal film during electromigration is reported in this paper. The electromigration process is modeled by a coupled diffusion- mechanical partial differential equations (PDEs). The PDEs are implemented with a plane strain formulation and numerically solved with the finite element (FE) method. The evolutions of hydrostatic stress, each component of the deviatoric stress tensor, and Von Mises' stress were simulated for several cases with different line lengths and current densities. Two types of displacement boundary conditions are considered. The simulation results are compared with Korhonen's analytical model and Black and Blech's experimentalesults.     

Modeling of multi-layered structure containing heterogeneous material layer with randomly distributed particles using infinite element method

In the electronics industry, filler particles are added to the epoxy to form a composite material in order to adjust the elastic modulus and the coefficient of thermal expansion (CTE). This paper enhances the infinite element method (IEM) for modeling and analyzing a multi-layered structure such as flip-chip assembly containing a heterogeneous material layer reinforced with randomly distributed multiple particles under thermal loading. The proposed method provides a straightforward and efficient means of modeling multiple particles since only one IE stiffness matrix of particle needs to be calculated for all of the other particles. Moreover, in analyzing the material interface problem, the proposed technique could put many number of element layers to measure the high stresses close to the edge of the multi-layered structure, and was easily applied to compare the maximum interfacial stresses near the corner.A series of problems relating to multi-layered structures containing heterogeneous materials are investigated. Initially, this study investigates the effect of varying the volume fraction of randomly arranged particles in the heterogeneous layer on the effective properties of the layer. The results obtained for the effective properties of the heterogeneous material and their influence on the interfacial stress are compared to those obtained from the Mori-Tanaka analytical method. Finally, in addition to equivalent models, three-dimensional finite element models containing multiple randomly distributed particles were built and studied. It is shown that at the free edge the interfacial stresses decrease when the number of particles close to the interface increases.     

Global interconnect design in a three-dimensional system-on-a-chip

A stochastic model for the global net-length distribution of a three-dimensional system-on-a-chip (3D-SoC) is derived. Using the results of this model, a global interconnect design window for a 3D-SoC is established by evaluating the constraints of: 1) wiring area; 2) clock wiring bandwidth; and 3) crosstalk noise. This window elucidates the optimum 3D-SoC global interconnect parameters for minimum pitch, minimum aspect ratio, and maximum clock frequency. In comparison to a two-dimensional system-on-a-chip (2D-SoC), the design window expands for a 3D-SoC to allow greater flexibility of interconnect parameters, thus increasing the guardbands to process variations. In addition, the limit on the maximum global clock frequency is revealed to increase as S/sup 2/, where S is the number of strata. This increase in on-chip signaling rate, however, comes at the expense of I/O density, highlighting the need for new high-density-I/O packaging techniques to exploit the full potential of 3D-SoC.     

工艺变化下互连线分布参数随机建模与延迟分析

随着超大规模集成电路制造进入深亚微米和超深亚微米阶段,电路制造过程中的工艺变化已经成为影响集成电路互连线传输性能的重要因素.文中引入高斯白噪声建立了互连线分布参数的随机模型,并提出基于Elmore延迟度量的工艺变化下的互连延迟估计式;通过简化工艺变化量与互连线参数之间的关系式,对延迟一阶变化量与二阶变化量进行了分析,给出一般工艺变化下互连延迟的统计特性计算方法;另,针对线宽工艺变化推导出互连延迟均值与方差的计算公式.最后通过仿真实验对工艺变化下互连线延迟分析方法及其统计特性计算公式的有效性进行了验证.     

Compact distributed RLC interconnect models-Part II: Coupled linetransient expressions and peak crosstalk in multilevel networks

For pt. I see ibid., vol. 47, no. 11, (Nov. 2000). Novel compact expressions that describe the transient response of high-speed resistance, inductance, and capacitance (RLC) coupled interconnects are rigorously derived. These new distributed rlc models reveal that peak crosstalk voltage is over 60% larger for 3 GHz high-speed interconnects than predicted by current distributed RC models. Simplified forms of the compact models enable physical insight and accurate estimation of peak crosstalk voltage between two and three distributed RLC interconnects     

Experimental study of electromigration at bamboo grain boundarieswith a new test structure using the single-crystal aluminuminterconnection

Electromigration (EM) voids in the bamboo structure interconnect were observed by a new test structure with single-crystal aluminum leads. The new test structure consists of a single grain connected to single-crystal aluminum leads formed by lateral-solid phase epitaxial growth (L-SPE). The grain was formed by suppressing L-SPE of the single-crystal aluminum leads. Since the void nucleation sites were confined to the grain boundaries, the voids were easily located and observed. In addition, the crystal orientation of single-crystal aluminum leads could be controlled by L-SPE, and so the analysis could be performed more accurately than using traditional test structures that have a series of grains with random crystal orientation. The accelerated EM test was carried out under ideal conditions similar to that of real devices, because the temperature gradients around the test site of the bamboo grain boundaries were negligible. In our preliminary experiment, a void was observed in the grain, located next to the positive voltage lead. This seems to be contradictory to general understandings, we think this is because of the grain boundary configuration difference and/or EM induced vacancy fluxes difference     

A turbo-like symbol by symbol decoder for randomly distributed space-time coding in amplify-and-forward relay networks

In this letter, a simple distributed Space-Time coding scheme is introduced by allocating random interleavers to each relay node in amplify-and-forward (AF) network. By using multiuser definition each rely node provides an interference to the detected signal, a turbo-like symbol by symbol decoder is also introduced. The complexity involved grows only linearly with the number of relay nodes. Simulation results show an acceptable improvement to previous works in the high SNR region.     

Preparation of randomly distributed micro-lens arrays fabricated from porous polymer film and their application as a light extraction component

We fabricated a randomly distributed micro-lens array (RDMLA) to improve the external quantum efficiency of organic light emitting diodes (OLED). We prepared three different types of RDMLA with different size distribution (L1 pattern: 0.3–0.5 μm, L2 pattern: 1.0–1.2 μm, L3 pattern: 3.0–5.0 μm). To control the average size of RDMLA, we prepared porous polymer film with an average pore size similar to that of RDMLA to utilize it as a template for simple imprinting technology. Especially, the RDMLA having L2 structure showed the best external quantum efficiency which was improved by 28.5% compared to that without RDMLA.     

Size effect in a percolation model of interconnect failure

The problem of interconnect failure is studied in the framework of percolation theory. The probability failure of a long interconnect due to statistical fluctuations of defects is found. It is demonstrated that two possible diapasons of length to width ratios exist. For extremely long wires, the percolation threshold is determined by rare accumulation of defects, breaking down the wire. For moderately long wires, the threshold concentration of defects is near the macroscopic percolation threshold. The lowering of threshold due to finite width of wire is found. The percolation threshold is found in a two-dimensional system, containing the individual vacancies and voids, caused by coalescence of vacancies.     

Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber

Distributed stress sensor with a white-light scanning interferometer is used to detect stress distribution by analyzing polarization mode coupling caused by forces exerted on PMFs (polarization maintaining fibers). In measurement of polarization coupling, the birefringence in sensing fiber is usually considered to be wavelength independent. Sensitivity and spatial resolution of the distributed stress sensor are constant for a given optical source spectrum. In practical measurement, however, the birefringence in PMFs is related with optical wavelength. In other words, birefringence dispersion exists in PMFs. Due to birefringence dispersion, the relationship between stress and coupling strength varies with different positions of external forces, and spatial resolution of the distributed stress sensor descends obviously with transmitted distance. In this paper, influences of external-force positions and optical source spectrum on distributed stress sensor are analyzed in consideration of birefringence dispersion and validated with experiments. A method for compensating birefringence dispersion in the sensing system is proposed in the end.     

Percolation and excitonic luminescence in SiO<Subscript>2</Subscript>/ZnO two-phase structures with a high density of quantum dots randomly distributed over a spherical surface

The results of studies of structures formed of silica (SiO₂) nanospheres and ZnO quantum dots randomly distributed over the nanosphere surface to cover an ∼0.45 fraction of the surface area are given. Because of the large surface energy of the spheres, the quantum dots formed on their surface are shaped as disks, wherein charge carriers are influenced by the quantum-confinement effect despite the large disk radii. The disk height is calculated by the effective mass method. The height is found to be comparable with the diameter of excitons in bulk ZnO. Analysis of the optical spectra shows that, at the above-indicated surface area covered with quantum dots, excitons in the array of quantum dots are above the percolation level. The use of some concepts of the percolation theory and knowledge of the topological arrangement of the samples make it possible to obtain quantitative parameters that describe this phenomenon.